Abstract
In this paper, moment inequalities for the new better than renwal used in Laplace transform order ( NBRUL ) class of ageing distributions are derived. This inequalities demonstrate that if the mean life is finite, then all higher order moments exist. A new test for exponentiality versus NBRUL can be constructed using thes inequalities. Pitman's asymptotic efficiencies and critical values of the proposed test are calculated and tabulated. The powers of this test are estimated for some famously alternatives distributions in reliability such as Linear failure rate,Weibull and gamma distributions. Finally, examples in different areas are used as a practical applications of the proposed test.
Highlights
Classes of life distributions are defined to classify the life distributions according to their aging properties
Testing exponentiality against IFR, new better than used (NBU) and NBUE based on moment inequalities have been studied by (Ahmad 2001); (Ahmad and Mugdadi 2004) constructed the tests of NBUC, IFRA and DMRL depends on the moment inequalities, while testing NRBU and RNBU based on moment inequalities have been studied by (Mahmoud, EL-arishy, and Diab 2003)
In this paper our theme formulates a new test statistic for testing exponentiality against NBRUL class based on the moment inequalities and discuss this test
Summary
Classes of life distributions are defined to classify the life distributions according to their aging properties. The definitions of these classes helped statisticians to define the test statistics. Many authors proposed tests for exponentiality versus some classes of life distributions based on the moment inequalities. Using the moment inequalities of the class NBUL, (Mahmoud, Diab, and Kayid 2009) constructed a test statistic for testing exponentiality versus this class. In this paper our theme formulates a new test statistic for testing exponentiality against NBRUL class based on the moment inequalities and discuss this test.
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